Question

The center of a circle is (4. 6) and its radius is 5. What is the equation of the circle?​

Answer 1

`(x - 4)^2 + (y - 6)^2 = 25.`

Explanation:

Start with the equation of a circle:
`(x - h)^2 + (y - k)^2 = r^2`

Plug in the values for the center:
`(x - 4)^2 + (y - 6)^2 = r^2`

Substitute the value of the radius:
`(x - 4)^2 + (y - 6)^2 = 5^2`

Simplify the equation:
`(x - 4)^2 + (y - 6)^2 = 25`

The resulting equation is the equation of the circle:
`(x - 4)^2 + (y - 6)^2 = 25.`

Answer 2

The equation of a circle with its center at point (h, k) and radius r is given by the formula:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (4, 6) and the radius is 5. Plugging these values into the equation, we get:

(x - 4)^2 + (y - 6)^2 = 5^2

Expanding the equation further:

(x - 4)^2 + (y - 6)^2 = 25

So, the equation of the circle is (x - 4)^2 + (y - 6)^2 = 25.